In this chapter, we discuss how our expanding space geometry generates basic physical concepts of mass and energy.

In the previous chapter, we discussed an expanding and closed geometry, where the expansion on spatial dimensions is uniform in all spatial directions. Point A, which is an arbitrary location on space in that geometry, flows towards time dimension perpendicular to space. We also discussed that the speed of flow is undeterminable, since it is a complete process of the whole, which leaves out no comparable entity. However, after deceleration of the increase in circumference’s size (space), there appear two related quantities having a determinable ratio.

Figure 5.11 The shortest distance in the wrinkling epoch

In the wrinkling epoch, point A still keeps on flowing from A₁ towards A₂ towards time dimension, since the fundamental tendency of expansion cannot be canceled even if it is pressurized. However, because of a stress mechanism, space and time dimension collapses onto itself, and the original path between A₁ to A₂ towards time dimension is deformed. Path of the flow from A₁ to A₂ is no longer perpendicular to spatial plane, and it follows oblique paths. For example:

1- In the confinement volume:

Flow of point A towards time dimension continues by following a helical path in a confined volume, with a constant angle (θ), which is less then 90 degrees, to the spatial plane.

2- Within the flux:

Electromagnetic radiation transfers energy in space-time by flowing within the expansion (the flux). However, since the expansion in all directions is strained universally, path of such energy packages flows towards the collapsed and proportioned direction. Light cone after a flash of light represents the proportioned (oblique) direction of the flux in the wrinkling epoch. In Chapter 8 on Quantum Mechanics, the exact meaning of the light cone will be discussed in further detail.

The expansion (the flux) has a new direction in space-time in the wrinkling epoch. Whether, the expansion continues in a confined volume or flows out in a direct motion, it has a constant angle (θ), which is less then 90 degrees, to the spatial plane.

Hence, the distance that a point flows towards spatial direction and the distance that it flows towards perpendicular time dimension has a determinable ratio. However, the ratio mentioned above is not the magnitude of the speed of light or the speed of the expansion (the flux). This ratio should NOT be confused with the constant of the speed of light, which is the constant relation between spatial distance metric and time as quantity of clock-ticks.

This ratio indicates the change in the direction of the expansion the (flux) from radial direction (time direction) to circumferential directions (spatial dimensions). In this paper, we will express this ratio also as an angle, which describes the obliquity of the wrinkled radial direction. In related mathematical equations, we will include it as the angle of radial obliquity (θradial obliquity).

Figure 5.12 The obliquity angle (θ)

This ratio of compression can also be considered as the ratio of the universal strain on the expansion, and it is a property of the current state of balance in the universe rather then a local property. The universal strain on the expansion indicates the ratio of the decelerated increase in the circumference (space) to the original linear expansion, but it does not describe the distribution of deformation on the space-time. Hence, its ratio is constant on the entire universe (similarly to Pascal’s principle).

Simply, it is the ratio between

A) the increase in the radius of the universe or the radius of the spatial curvature of the universe (increase in the overall size of the tree),

and

B) the distance that the expansion (the flux) flows (increase in the length of the branches).

This ratio also indicates the proportion between

A) the increase in the spatial size of the universe according to Hubble’s expansion,

and

B) the distance that light travels.

Practically, this ratio generates the most fundamental constant in Nature, which cannot be removed by a properly designed natural unit system.

According to this paper, the total matter content in the universe was not determined at the Big Bang, and it was not scattered because of a mysteriously embedded energy potential. Matter was formed against the universal strain on the expansion.

Therefore, total matter-energy content in the universe is related to the ratio of the universal strain on the expansion, and its quantity depends on the ratio mentioned in the previous section.

We will develop these predictions after additional discussions in the following chapters. However, it is now time to examine the meanings of distance and time in physical reality. As a result, we will see how this paper develops the relativity phenomenon, and derive gamma of the Lorentz transformation equations as a natural result of its hypothesis.